If a, b, c, d are in G.P, prove that :

Question

Philoid · Accepted Answer

a, b, c, d are in G.P.

Let r be the common ratio.

Therefore,

b = ar …(1)

c = ar² …(2)

and d = ar³ …(3)

If somehow we use LHS and Make it equal to RHS, our job will be done.

we can manipulate the LHS of the given equation as –

⇒ LHS =

Put the values of a,b,c and d from equation 1,2 and 3

⇒ LHS =

Multiplying a in numerator and denominator –

⇒ LHS =

Again from equation 1, 2, and 3, we can see –

LHS = = RHS …hence proved